A parliamentary system with fully proportional representation would be best. The US is big though, so I think an electoral threshold of 4% may be needed. That, or require parties to fulfil the below condition before being able to participate in elections.
• They need enough support through party membership from the area's population, as a % of the latter. On counties, this would be about 4%. On a state level, that would be 1%. On a national level, 0.25% would be enough.
You might think, why lower with each level? But the larger the population size is, the smaller the membership can be while remaining representative. This also stimulates smaller parties since now they have a chance to actually grow.
Electoral districts also need to be thrown away -- counties, states, and the entire country, are where the elections get held in. Because of proportional representation, it doesn't matter however you were to divide up areas: 25% of votes on one party means 25% of seats.
Lastly, force the Democratic and Republican Party to break up into separate parties with each no more than 20% of all seats. Or tell the parties that putting through with proportional representation as an agenda point will give them more votes. The Dems can argue, "One man, one vote", the Reps can argue "America NEEDS to keep it Great! Vote the Dems away, get Proportional!". Both should have this as agenda point.
I also think it critical that the supreme court of the US isn't 7 judges. It worked for a country with 2 million people, but you lot are a country of 300+ million now. You need something like 100 members, and make the supreme court appointed by the judges themselves, who are chosen by multiple random ballots themselves.
The US Congress also could be expanded. Make the House go from 435 to 500 members, and the Senate to 250. They need to be updated for a big country.
It also makes it harder to manipulate politicians, since there are far more needed to bribe.
I have a whole writeup, if anyone is interested. I think that both Dems and Reps and anyone else can find themselves in it.